Chalcogenide glass microspheres for biosensing

Many photonic devices for biosensing are based on optical microresonators, such as the Fabry-Pérot. These systems use mirrors to achieve light oscillation in an optical cavity and produce output signals that depend on the chemicals present in the cavity. However, such microresonators have drawbacks, including high cost, limited compactness, and mechanical instability.¹ One alternative approach is to use dielectric microspheres, which enable the confinement of light in circular orbits close to the spherical boundary (whispering gallery modes, or WGMs) between the dielectric surface and the surrounding medium. WGMs exhibit resonances with high quality factors Q (10⁵/10⁹)—meaning a lower rate of energy loss—and small mode volumes, making them suitable for use in lasers, add-drop filters, or biochemical sensors.^2–5 WGMs in dielectric microspheres already have applications in polarization transmission (for polarization converters), coupled-resonator-induced transparency (for obtaining optical information storage), biosensing, nonlinear optics, quantum electrodynamics, and quantum information processing.^6–8 They enable novel functionalities in integrated optics, such as wavelength selectivity, energy storage and dispersion control, and resonant filtering.⁹ Moreover, when doped with rare earth ions, microspheres can operate as amplifiers or microcavity lasers with low threshold lasing. Therefore, they enable light generation with low-power pumping, and the very narrow emission linewidths required in applications such as spectroscopy or sensing.^10–14

Several optical devices use microspheres of chalcogenide glass.^15–19 Chalcogenide has a high refractive index, high nonlinearity, photosensitivity, low phonon energy, large radiative decay rates, high quantum efficiency, and enables emissions in the mid-IR at wavelengths that cannot be achieved with conventional silica glass. The low phonon energy (excitation of atoms or molecules) in chalcogenide glasses enables high transition rates, long lifetimes of excited dopant ions, low background losses, and induces reduced multiphonon relaxation.^15–18 As a result, it is possible to obtain mid-IR, low-threshold lasers with suitably designed rare-earth-doped chalcogenide microspheres.^19–30

WGMs in such spheres are coupled by tapered silica fibers using evanescent electromagnetic fields from waveguides placed nearby. To achieve this on planar geometry and in a suitably packaged format, we produced microsphere prototypes of chalcogenide glass composed of gallium, germanium, antimony, and sulfur (Ga₅Ge₂₀Sb₁₀S₆₅) and doped the spheres with erbium (Er). We used the surface-tension mold (StM) technique, which makes use of the wetting properties between a glass melt and a substrate,²⁰ to fabricate partly truncated spheres. The StM technique enabled formation of a superspherical shape with a diameter of 5–50μm (see Figure 1). The contact angle (the angle at which liquid and solid surface meet) of such glass is θ>90°, since glassy carbons present a favorable substrate to induce low wettability of molten chalcogenide glass.²¹ Using a Raman spectrophotometer, we observed WGMs in these microspheres for emissions in the visible range, and we also experimentally observed luminescence in the mid-IR range from Er³⁺:Ga₅Ge₂₀Sb₁₀S₆₅ glass,³¹ including emission at 2775nm corresponding to the ⁴I_11/2 → ⁴I_13/2 transition. Based on these observations we demonstrated lasing in microspheres made of Er³⁺:Ga₅Ge₂₀Sb₁₀S₆₅. To design (or characterize) our prototypes (including optimal amplifier radius, rare earth concentration, and waveguide transversal section), we considered particle swarm optimization (PSO) modeling, a computational method for problem solving based on ‘ swarm’ behavior of particles that represent possible solutions.²¹ We chose PSO because solving equations relating to rate of ion transitions and power propagation using conventional numerical procedures requires the optimization of each design parameter, one by one.^22–24 For our rare-earth-doped model it was difficult to perform such optimization because the up-conversion and cross-relaxation phenomena (the energy transfer between dopant ions) induce nonlinearities. Furthermore, deterministic algorithms can exhibit stagnation problems in local maxima/minima during the optimization search for the objective functions (in this case, gain or output power). The PSO algorithm, due to its stochastic nature, is highly efficient in optimizing a large number of parameters, can avoid local maxima/minima, and can operate in discontinuous solution domains.^{25–27, 32}

Figure 1. Images taken with an optical microscope (left) and scanning electron microscope (right) of an erbium-doped microsphere of chalcogenide glass (Ga₅Ge₂₀Sb₁₀S₆₅) coated with a gold/palladium conductive layer at the surface to assist imaging.²¹

Using PSO, we optimized an amplifying system operating close to 2.7μm and based on Er³⁺-doped chalcogenide microspheres coupled to a tapered fiber.²¹ We used a 3D mathematical model^{28, 29} to calculate the fitness function of the PSO procedure,^25–27 employing the optical and spectroscopic parameters measured on chalcogenide glass,^{29, 30} and on fabricated and characterized preliminary samples of microspheres.²¹

We modeled an amplifying system comprising a tapered optical fiber placed close to the equator of Er³⁺-doped chalcogenide microspheres, with²¹ and without²⁸ PSO, and modeled the coupling of the optical power between the tapered fiber and the undoped microspheres.^33–35 We obtained time-domain evolution of the amplitude of the internal cavity electromagnetic field at the pump and the signal wavelength by solving the pertaining differential equations.^{28, 34–39}

We performed the PSO design for a pump wavelength close to λ_p=980nm and a signal wavelength close to λ_s=2770nm.²¹ The thickness of the Er-doped region and the Er concentration were s=3μm and N_Er=0.5wt%, respectively. The input pump power was P_p=100mW and the input signal power P_s=−50dBm.

To perform the PSO simulations, we considered many WGMs in the wavelength band 2740–2820nm. The PSO enabled identification of the maximum gain (global best) for the WGM_{1, 217, 217} with the following optimal parameters: microsphere radius R₀=45μm, taper waist radius a=517nm, taper angle δ=0.03rad, taper-microsphere gap g=512nm. By varying the parameter n from 1 to 3, we simulated 18 different resonant WGMs.

For each WGM, we took into account the proper resonance frequency to consider all the spectroscopic and physical parameters (refractive index, emission cross section, and absorption cross section) that would affect the competition with other WGMs. The use of a deterministic method required a suitable discretization for R₀, a, δ, g, and thus the investigation of an extremely high number of different cases.²⁸ PSO, by contrast, optimizes simultaneously a high number of parameters through an automated global solution search. The discrepancy in the calculated maximum gain observed using the two different optimization methods (deterministic, G=6.9dB, and PSO-based, G=33.7dB) is due to the higher efficiency of the global optimization approach.

In conclusion, we have designed an Er³⁺-doped chalcogenide microsphere amplifier evanescently coupled with a tapered optical fiber. We optimized the amplifying system using a PSO procedure for operation close to 2770nm, and fabricated preliminary chalcogenide microspheres. The PSO approach and StM technique promise good results in the design and fabrication of active and passive microspheres, which could find applications in optical sensing for biomedicine.

Microspheres of Ga₅Ge₂₀Sb₁₀S₆₅ have previously been fabricated and characterized. However, building an amplifier requires a suitable Ga₅Ge₂₀Sb₁₀S₆₅ fiber taper with a very small radius. Future work will focus on obtaining such a taper, or on designing a coupling integrated optical system.³¹ We will also investigate the feasibility of chalcogenide microspheres obtaining amplification and lasing in the mid-IR wavelength range. We will use the PSO algorithm to form the design, and will extend the work to include different kinds of glass (ZBLAN, silica, tellurite, and chalcogenide, for example) and different dopants (dysprosium, praseodymium, or neodymium). Moreover, the code will allow the design of microsphere resonators with different layers/packages with complex refractive indexes. Only some of these materials will be considered for mid-IR operation (chalcogenide and tellurite glasses, for example), while the other materials will be tested for comparison and theoretically investigated for their wavelength range operation. We will examine coupling with fiber tapers that have both microstructured and conventional sections, and may consider the integration of planar waveguides.⁴⁰